I need help with this problem,
$$\int_0^4|x^2 - 2|x||dx$$
what should I do with $2|x|$ ?
2026-04-02 12:46:24.1775133984
How to integrate a function with a nested absolute value: $|x^2 - 2|x||$?
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Conveniently, your integration limits are $(0,4)$ so the inside absolute value can be ignored. You are left with the following: $$\int_0^4 |x^2 - 2x| \ dx = \int_0^4x\cdot|x-2|\ dx$$ $$= \int_0^2 x\cdot(2-x)\ dx + \int_2^4x\cdot(x-2) \ dx$$ I leave the rest to you.